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Solving Black And White: (Opposite Pairs)

This is a very useful technique of solving Black And White puzzle. Take a look at the two images below.
This situation cannot occur anywhere in any Black And White puzzle! Suppose you find such a situation in a 2x2 region. When you try joining the two white circles, one black circle will be blocked from the other in either way. The same works vice-versa.

Take a look at Puzzle No.341

Try solving as much as possible without guessing.


If you do not know this technique, you may place a white circle at R1C2 and then start scratching your head. Using this technique makes this puzzle a level one puzzle :-)


Take a look at the marked 2x2 region. Since the Opposite Pairs situation cannot occur, R3C2 has to be a black circle.


Using the 2x2 constraint, R4C1 is a white circle.


Using the Edge Connection Technique, the entire edge can be made white.


Using the 2x2 constraints, some more circles can be place.


You should be able to complete it using simple logic.

Now when you look back, I'm sure you will realise how easy this puzzle is with the Opposite Pairs Technique :-)

Other Solving Techniques

6 comments:

Rajesh Kumar said...

Thanks for this technique. I was not knowing this and always finding this puzzle type a tough one. Now it looks very easy puzzle type

Rohan Rao said...

Rajesh, I wonder how you won IPC so many times! :D

Tejal Phatak said...

Superb! :)

Aman Pruthi said...

Since whole 2010 Indian WPC team commented, I thought I'll also.

But it's a great technique, I too never thought of it.

Missing puzzles alot :(, once I get through with a new job, I'll be back.

Rohan Rao said...

Wow! The lost man is here...

Get back soon, you need to solve puzzles so that you miss your job :P

hariniraman said...

I have another technique apart from these 2 that you have mentioned, that is quite useful in certain puzzles. You might be interested in adding it to your blog.
And btw, good job on the blog. I find it very useful :)